Publication

Nonlinear weighted residual approach: application to laminated beams

2003
Journal Articles

Abstract

A weighted residual formulation of equilibrium equations for nonlinear structural analysis is presented in material description. Starting from the strong form, the weak form is derived by means of a suitable choice of weighting functions. In order to get the tangent stiffness matrix of the finite element approximation, the weak form is first linearized and then discretized. This sequence is well suited when large displacement fields nonlinearly depend on degrees of freedom, which currently occurs in structures.

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2003
Journal Articles

Abstract

Official source

Related concepts (32)

Linear least squares

Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals. Numerical methods for linear least squares include inverting the matrix of the normal equations and orthogonal decomposition methods. The three main linear least squares formulations are: Ordinary least squares (OLS) is the most common estimator.

Least squares

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.

Structural analysis

Structural analysis is a branch of solid mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on the physical structures and their components. In contrast to theory of elasticity, the models used in structure analysis are often differential equations in one spatial variable. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, aircraft and ships.

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Nonlinear weighted residual approach: application to laminated beams

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